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[linpy.git] / examples / squares.py
1 #!/usr/bin/env python3
2
3 from linpy import *
4 import matplotlib.pyplot as plt
5 from matplotlib import pylab
6
7 a, x, y, z = symbols('a x y z')
8
9 sq1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
10 sq2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
11 sq3 = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3)
12 sq4 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 2)
13 sq5 = Le(1, x) & Le(x, 2) & Le(1, y)
14 sq6 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 3)
15 sq7 = Le(0, x) & Le(x, 2) & Le(0, y) & Eq(z, 2) & Le(a, 3)
16 p = Le(2*x+1, y) & Le(-2*x-1, y) & Le(y, 1)
17
18 universe = Polyhedron([])
19 q = sq1 - sq2
20 e = Empty
21
22 print('sq1 =', sq1) #print correct square
23 print('sq2 =', sq2) #print correct square
24 print('sq3 =', sq3) #print correct square
25 print('sq4 =', sq4) #print correct square
26 print('universe =', universe) #print correct square
27 print()
28 print('¬sq1 =', ~sq1) #test complement
29 print()
30 print('sq1 + sq1 =', sq1 + sq2) #test addition
31 print('sq1 + sq2 =', Polyhedron(sq1 + sq2)) #test addition
32 print()
33 print('universe + universe =', universe + universe)#test addition
34 print('universe - universe =', universe - universe) #test subtraction
35 print()
36 print('sq2 - sq1 =', sq2 - sq1) #test subtraction
37 print('sq2 - sq1 =', Polyhedron(sq2 - sq1)) #test subtraction
38 print('sq1 - sq1 =', Polyhedron(sq1 - sq1)) #test subtraction
39 print()
40 print('sq1 ∩ sq2 =', sq1 & sq2) #test intersection
41 print('sq1 ∪ sq2 =', sq1 | sq2) #test union
42 print()
43 print('sq1 ⊔ sq2 =', Polyhedron(sq1 | sq2)) # test convex union
44 print()
45 print('check if sq1 and sq2 disjoint:', sq1.isdisjoint(sq2)) #should return false
46 print()
47 print('sq1 disjoint:', sq1.disjoint()) #make disjoint
48 print('sq2 disjoint:', sq2.disjoint()) #make disjoint
49 print()
50 print('is square 1 universe?:', sq1.isuniverse()) #test if square is universe
51 print('is u universe?:', universe.isuniverse()) #test if square is universe
52 print()
53 print('is sq1 a subset of sq2?:', sq1.issubset(sq2)) #test issubset()
54 print('is sq4 less than sq3?:', sq4.__lt__(sq3)) # test lt(), must be a strict subset
55 print()
56 print('lexographic min of sq1:', sq1.lexmin()) #test lexmin()
57 print('lexographic max of sq1:', sq1.lexmax()) #test lexmin()
58 print()
59 print('lexographic min of sq2:', sq2.lexmin()) #test lexmax()
60 print('lexographic max of sq2:', sq2.lexmax()) #test lexmax()
61 print()
62 print('Polyhedral hull of sq1 + sq2 is:', q.aspolyhedron()) #test polyhedral hull
63 print()
64 print('is sq1 bounded?', sq1.isbounded()) #bounded should return True
65 print('is sq5 bounded?', sq5.isbounded()) #unbounded should return False
66 print()
67 print('sq6:', sq6)
68 print('sample Polyhedron from sq6:', sq6.sample())
69 print()
70 print('sq7 with out constraints involving y and a', sq7.project([a, z, x, y]))
71 print()
72 print('the verticies for s are:', p.vertices())
73
74
75 # plotting the intersection of two squares
76 square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
77 square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
78
79 fig = plt.figure()
80 plot = fig.add_subplot(1, 1, 1, aspect='equal')
81 square1.plot(plot, facecolor='red', alpha=0.3)
82 square2.plot(plot, facecolor='blue', alpha=0.3)
83
84 squares = Polyhedron(square1 + square2)
85 squares.plot(plot, facecolor='blue', alpha=0.3)
86
87 pylab.show()